Transmission electron microscopy is an indispensable tool in modern materials science. It enables the structure of materials to be studied with high spatial resolution, and thus makes a decisive contribution to the fact that it is now possible to understand the microstructure-related physical and chemical characteristics and to correlate these with the macroscopic materials properties. It was tantamount to a paradigm shift when electron microscopy reached atomic resolution in the late 1990s due to the invention of aberration-corrected electron optics. It is now generally accepted practice to perform picometer-scale measurements and chemical analyses with reference to single atomic units. This review has three objectives. Microscopy in atomic dimensions is applied quantum physics. The consequences of this for practical work and for the understanding and application of the results shall be worked out. Typical applications in materials science will be used to show what can be done with this kind of microscopy and where its limitations lie. In the absence of relevant monographs, the aim is to provide an introduction to this new type of electron microscopy and to enable the reader to access the literature in which special issues are addressed. The paper begins with a brief presentation of the principles of optical aberration correction. It then discusses the fundamentals of atomic imaging and covers typical examples of practical applications to problems in modern materials science. It is emphasized that in atomic-resolution electron microscopy the quantitative interpretation of the images must always be based on the solution of the quantum physical and optical problem on a computer.